{"id":26877,"date":"2021-10-08T13:00:17","date_gmt":"2021-10-08T13:00:17","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26877"},"modified":"2024-05-27T02:37:27","modified_gmt":"2024-05-27T02:37:27","slug":"%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9%d8%a7%d8%aa-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d9%8a%d8%a9-%d8%a7%d9%84%d9%85%d8%b3%d8%aa%d9%85%d8%b1%d8%a9","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9%d8%a7%d8%aa-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d9%8a%d8%a9-%d8%a7%d9%84%d9%85%d8%b3%d8%aa%d9%85%d8%b1%d8%a9\/","title":{"rendered":"\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0645\u0644\u062e\u0635<\/strong><br \/><em>\u0647\u0646\u0627 \u0633\u0646\u0642\u0648\u0645 \u0628\u0641\u062d\u0635 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0628\u0639\u0645\u0642\u060c \u0645\u0633\u0644\u0637\u064a\u0646 \u0627\u0644\u0636\u0648\u0621 \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u0648\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a \u0627\u0644\u062e\u0645\u0633 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629: \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0627\u0644\u062c\u0648\u0633\u064a)\u060c \u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644 \u0648\u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627. \u0633\u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u0644 \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a\u060c \u0648\u0633\u064a\u062a\u0645 \u0641\u062d\u0635 \u0627\u0644\u0622\u062b\u0627\u0631 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0644\u0647\u0627\u060c \u0645\u062b\u0644 \u062a\u0642\u064a\u064a\u0645 \u0627\u0646\u0628\u0639\u0627\u062b \u0627\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u0641\u064a \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0634\u0639\u0629 \u0623\u0648 \u062d\u0633\u0627\u0628 \u0645\u0648\u0642\u0639 \u0643\u0631\u0629 \u0639\u0644\u0649 \u0633\u0643\u0629 \u0628\u062d\u062f\u0648\u062f. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u064a\u062a\u0645 \u062a\u0641\u0635\u064a\u0644 \u0643\u064a\u0641\u064a\u0629 \u062a\u0639\u062f\u064a\u0644 \u0648\u062a\u0643\u064a\u064a\u0641 \u0647\u0630\u0647 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0637\u0628\u064a\u0642 \u0645\u0639\u0644\u0645\u0627\u062a \u0645\u062d\u062f\u062f\u0629.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\u0628\u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649:\n<\/p>\n<ol>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0645\u0627 \u0647\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629: \u0627\u0644\u0623\u0633\u064a\u060c \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u060c \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0627\u0644\u062c\u0648\u0633\u064a)\u060c \u0648\u064a\u0628\u0644\u060c \u0648\u062c\u0627\u0645\u0627.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u0645\u0627 \u0647\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629\u061f<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u0627\u0644\u062e\u0645\u0633 \u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629<\/strong><\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a<\/a><br \/>\n<a href=\"#4\">\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644 \u0627\u0644\u0645\u0646\u062a\u0638\u0645<\/a><br \/>\n<a href=\"#5\">\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0627\u0644\u062c\u0648\u0633\u064a)<\/a><br \/>\n<a href=\"#6\">\u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644<\/a><br \/>\n<a href=\"#7\">\u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627<\/a><br \/>\n<a href=\"#8\"><strong>\u062a\u0645\u0627\u0631\u064a\u0646<\/strong><\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/REOTUa7K8uQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u0639\u0646\u062f \u0645\u0631\u0627\u062c\u0639\u062a\u0646\u0627 \u0644\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0640<a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%aa%d8%b9%d8%b1%d9%91%d9%81-%d8%b9%d9%84%d9%89-%d8%a7%d9%84%d9%81%d8%b6%d8%a7%d8%a1-%d8%a7%d9%84%d8%b9%d9%8a%d9%86%d9%8a-%d9%81%d9%8a-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa\/\" target=\"_blank\" rel=\"noopener\">\u0641\u0636\u0627\u0621\u0627\u062a \u0627\u0644\u0639\u064a\u0646\u0629<\/a> \u0631\u0623\u064a\u0646\u0627 \u0623\u0646 \u0647\u0630\u0647 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0646 \u0646\u0648\u0639\u064a\u0646: \u0646\u0648\u0639 \u0645\u062a\u0642\u0637\u0639 \u0648\u0622\u062e\u0631 \u0645\u0633\u062a\u0645\u0631. \u0643\u0645\u0627 \u0631\u0627\u062c\u0639\u0646\u0627 \u0645\u0627 \u064a\u0634\u0643\u0644 <a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d8%aa%d9%88%d8%b2%d9%8a%d8%b9%d8%a7%d8%aa-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85%d8%a7%d9%84%d9%8a%d8%a9-%d8%a7%d9%84%d9%85%d9%86%d9%81%d8%b5%d9%84%d8%a9-%d9%88%d8%a7%d9%84%d8%a3%d9%85\/\" target=\"_blank\" rel=\"noopener\">\u062a\u0648\u0632\u064a\u0639 \u0627\u062d\u062a\u0645\u0627\u0644\u064a \u0645\u062a\u0642\u0637\u0639<\/a>. \u0627\u0644\u0622\u0646 \u062c\u0627\u0621 \u062f\u0648\u0631 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629.<\/p>\n<p>&nbsp;<\/p>\n<p><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u0645\u0627 \u0647\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629\u061f<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=86s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0646\u0642\u0648\u0644 \u0623\u0646 \u0645\u062a\u063a\u064a\u0631\u064b\u0627 \u0639\u0634\u0648\u0627\u0626\u064a\u064b\u0627<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0644\u062f\u064a\u0647 \u062a\u0648\u0632\u064a\u0639 \u0627\u062d\u062a\u0645\u0627\u0644\u064a \u0645\u0633\u062a\u0645\u0631 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0646\u0627\u0643 \u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X : \\mathbb{R} \\longrightarrow \\mathbb{R}^+,<\/span><\/span> \u0627\u0644\u062a\u064a \u0633\u0646\u0633\u0645\u064a\u0647\u0627 <strong>\u0643\u062b\u0627\u0641\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X,<\/span><\/span><\/strong> \u0628\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\forall A \\subseteq \\mathbb{R}<\/span><\/span> \u064a\u0643\u0648\u0646 \u0635\u062d\u064a\u062d\u064b\u0627 \u0623\u0646<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X\\in A) = \\displaystyle \\int_A f_X(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u0625\u0630\u0627 \u0623\u062e\u0630\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=]a,b]<\/span><\/span> \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(a\\lt X \\leq b) = \\displaystyle \\int_a^b f_X(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=-\\infty<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x) = P( X \\leq x) = \\displaystyle \\int_{-\\infty}^x f_X(t)dt<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0623\u064a\u0636\u064b\u0627\u060c \u0645\u0646 \u062e\u0627\u0635\u064a\u0629 (c) \u0644\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 (<a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%85%d8%aa%d8%ba%d9%8a%d8%b1%d8%a7%d8%aa-%d8%a7%d9%84%d8%b9%d8%b4%d9%88%d8%a7%d8%a6%d9%8a%d8%a9-%d9%88%d8%aa%d9%88%d8%b2%d9%8a%d8%b9%d8%a7%d8%aa-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85\/\" rel=\"noopener\" target=\"_blank\">\u0627\u0646\u0638\u0631 \u0647\u0646\u0627<\/a>) \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0623\u0646<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty} f_X(t)dt = 1<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0628\u062a\u0637\u0628\u064a\u0642 \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0623\u062e\u064a\u0631\u060c \u064a\u0643\u0648\u0646 \u0623\u0646 \u062a\u0648\u0632\u064a\u0639 \u0645\u0633\u062a\u0645\u0631\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x),<\/span><\/span> \u064a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u064b\u0627 \u0644\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,<\/span><\/span> \u0648\u0645\u0634\u062a\u0642\u062a\u0647 \u0647\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X(x)<\/span><\/span> \u0644\u0643\u0644 \u0627\u0644\u0642\u064a\u0645 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X(x)<\/span><\/span> \u064a\u0643\u0648\u0646 \u0645\u0633\u062a\u0645\u0631\u064b\u0627. \u0645\u0646 \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x)<\/span><\/span> \u0648\u0645\u0646 \u062e\u0627\u0635\u064a\u0629 (d) (<a href=\"http:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%85%d8%aa%d8%ba%d9%8a%d8%b1%d8%a7%d8%aa-%d8%a7%d9%84%d8%b9%d8%b4%d9%88%d8%a7%d8%a6%d9%8a%d8%a9-%d9%88%d8%aa%d9%88%d8%b2%d9%8a%d8%b9%d8%a7%d8%aa-%d8%a7%d9%84%d8%a7%d8%ad%d8%aa%d9%85\/\" rel=\"noopener\" target=\"_blank\">\u0627\u0646\u0638\u0631 \u0647\u0646\u0627<\/a>) \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x=X)=0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x\\leq X)= P(x\\lt X)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> \u0623\u064a \u062f\u0627\u0644\u0629 \u062a\u062d\u0642\u0642 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\geq 0<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty}f(x)dx = 1,<\/span><\/span> \u0641\u0625\u0646\u0647\u0627 \u062a\u0633\u0645\u0649 \u0643\u062b\u0627\u0641\u0629.<\/p>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>\u0627\u0644\u062e\u0645\u0633 \u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629<\/h2>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=714s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a<\/span><\/strong><\/a> \u0645\u0639 \u0645\u0639\u0644\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha \\gt 0 <\/span><\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F<\/span><\/span> \u0628\u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a.<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(t) = \\left\\{\\begin{array}{lll}\n\n1 - e^{-t\/\\alpha} &amp; ; &amp; t\\geq 0 \\\\ \\\\\n\n0 &amp; ; &amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0647\u064a \u0628\u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(t) = \\left\\{\\begin{array}{lll}\n\n\\frac{1}{\\alpha}e^{-t\/\\alpha} &amp; ; &amp; t\\geq 0 \\\\ \\\\\n\n0 &amp; ; &amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u0623\u0633\u064a \u0645\u0639 \u0645\u0639\u0644\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u0646\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Ex(\\alpha).<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0641\u064a \u0633\u064a\u0627\u0642 \u062a\u0648\u0632\u064a\u0639 \u0628\u0648\u0627\u0633\u0648\u0646\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0639\u064a\u0646\u0629 \u0645\u0634\u0639\u0629 \u062a\u0628\u0639\u062b \u062c\u0633\u064a\u0645\u064b\u0627 \u0628\u0645\u0639\u062f\u0644 \u0645\u062a\u0648\u0633\u0637 \u0644\u0644\u0625\u0635\u062f\u0627\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c,<\/span><\/span> \u0641\u0625\u0646 \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T<\/span><\/span> \u0627\u0644\u062a\u064a \u064a\u0646\u0628\u0639\u062b \u0641\u064a\u0647\u0627 \u0627\u0644\u062c\u0633\u064a\u0645 \u0627\u0644\u0623\u0648\u0644 \u064a\u0643\u0648\u0646 \u0644\u0647\u0627 \u062a\u0648\u0632\u064a\u0639 \u0623\u0633\u064a \u0628\u0645\u0639\u0644\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1\/c.<\/span><\/span> \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T\\sim Ex(1\/c),<\/span><\/span> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(T\\geq t)= e^{-ct}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644 \u0627\u0644\u0645\u0646\u062a\u0638\u0645<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=930s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0648\u0632\u064a\u0639 \u0645\u0633\u062a\u0637\u064a\u0644 \u0645\u0646\u062a\u0638\u0645<\/span><\/strong><\/a> \u0639\u0644\u0649 \u0641\u062a\u0631\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0647\u0648 \u0627\u0644\u0630\u064a \u064a\u0639\u0631\u0641 \u0628\u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u062b\u0627\u0641\u0629<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\left\\{\\begin{array}{lll}\n\n\\displaystyle\\frac{1}{b-a} &amp; ; &amp; x\\in[a,b] \\\\ \\\\\n\n0 &amp; ; &amp; \u0623\u064a \u062d\u0627\u0644\u0629 \u0623\u062e\u0631\u0649\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0623\u0633\u0642\u0637\u0646\u0627 \u0643\u0631\u0629 \u0635\u063a\u064a\u0631\u0629 \u0641\u064a \u0633\u0643\u0629 \u0628\u062d\u062f\u0648\u062f \u0641\u064a \u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0641\u062a\u0631\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u0648\u0627\u0631\u062a\u062f\u062a \u0628\u0645\u0631\u0648\u0646\u0629 \u0639\u0646\u062f \u0627\u0644\u0627\u0635\u0637\u062f\u0627\u0645 \u0628\u0627\u0644\u062d\u0648\u0627\u0641\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0627\u0644\u0645\u0631\u062a\u0628\u0637 \u0628\u0645\u0648\u0642\u0639 \u062a\u0648\u0642\u0641 \u0627\u0644\u0643\u0631\u0629 \u0628\u0641\u0639\u0644 \u0627\u0644\u0627\u062d\u062a\u0643\u0627\u0643 \u064a\u0643\u0648\u0646 \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u0645\u0633\u062a\u0637\u064a\u0644 \u0645\u0646\u062a\u0638\u0645 \u0648\u064a\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Un(a,b)<\/span>.<\/span><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h3>\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0627\u0644\u062c\u0648\u0633\u064a)<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1109s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0645\u0646 \u0628\u064a\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629<\/span><\/strong><\/a>\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0647\u0648 \u0645\u0646 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629 \u0641\u064a \u0627\u0644\u0645\u0645\u0627\u0631\u0633\u0629.<\/p>\n<h4>\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1150s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629<\/span><\/strong><\/a> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062f\u0627\u0644\u0629<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\phi_{0,1}(x) = \\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0628\u062a\u0639\u0631\u064a\u0641\u0647\u0627\u060c \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi\\gt 0.<\/span><\/span> \u0644\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0623\u0646\u0647\u0627 \u0643\u062b\u0627\u0641\u0629 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0628\u0628\u0633\u0627\u0637\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0623\u0646<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty}\\phi_{0,1}(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0623\u062e\u064a\u0631\u0629 \u0628\u062d\u0633\u0627\u0628 \u0642\u064a\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I^2<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I =\\int_{-\\infty}^{+\\infty}\\phi(x)dx=1.<\/span><\/span> \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0644\u062f\u064a\u0646\u0627:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nI^2 &amp; = \\displaystyle \\int_{-\\infty}^{+\\infty}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2} dx \\int_{-\\infty}^{+\\infty}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2}dx \\\\ \\\\\n\n&amp; = \\displaystyle \\int_{-\\infty}^{+\\infty}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2} dx \\int_{-\\infty}^{+\\infty}\\frac{1}{\\sqrt{2\\pi}} e^{-y^2\/2} dy \\\\ \\\\\n\n&amp; = \\displaystyle \\frac{1}{{2\\pi}} \\int_{-\\infty}^{+\\infty} \\int_{-\\infty}^{+\\infty} e^{-\\frac{x^2 + y^2}{2}} dxdy \\\\ \\\\\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0644\u0643\u0646 \u064a\u062a\u0636\u062d \u0623\u0646<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\int_{-\\infty}^{+\\infty} \\int_{-\\infty}^{+\\infty} e^{-\\frac{x^2 + y^2}{2}} dxdy = \\int_{0}^{2\\pi} \\int_{0}^{+\\infty} e^{-r^2\/2} rdr d\\theta = 2\\pi <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I^2 = 1,<\/span><\/span> \u0628\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I=\\int_{-\\infty}^{+\\infty}\\phi_{0,1}(x)dx = 1. <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0645\u0646 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629 \u064a\u062a\u0645 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(x) = \\int_{-\\infty}^x\\phi_{0,1}(t)dt.<\/span><\/span> \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a \u0645\u0639\u064a\u0627\u0631\u064a\u060c \u0641\u0625\u0646\u0647 \u064a\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim N(0,1).<\/span><\/span> \u0627\u0644\u062a\u0648\u0632\u064a\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(x)<\/span><\/span> \u0644\u0627 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647 \u0628\u0634\u0643\u0644 \u0635\u0631\u064a\u062d\u060c \u0648\u0644\u0643\u0646 \u0647\u0646\u0627\u0643 \u062c\u062f\u0627\u0648\u0644 \u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0642\u064a\u0645 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0628\u0633\u0631\u0639\u0629.<\/p>\n<h4>\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma<\/span><\/span><\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1875s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0645\u0646 \u0643\u062b\u0627\u0641\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_{0,1}<\/span><\/span> \u064a\u0645\u0643\u0646 \u0628\u0646\u0627\u0621 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma,<\/span><\/span> \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu\\in\\mathbb{R}<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma\\gt 0 <\/span><\/span> \u0647\u064a \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a\u060c \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0648\u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a. \u0643\u062b\u0627\u0641\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0628\u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a \u062a\u0643\u062a\u0628 \u0628\u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\phi_{\\mu,\\sigma}(x) = \\frac{1}{\\sigma}\\phi_{0,1}\\left(\\frac{x-\\mu}{\\sigma} \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0628\u062d\u064a\u062b \u0623\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{\\mu,\\sigma}(x)<\/span><\/span>\u060c \u062a\u0643\u062a\u0628 \u0628\u0627\u0644\u0634\u0643\u0644<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Phi_{\\mu,\\sigma}(x) = \\int_{-\\infty}^x\\frac{1}{\\sigma}\\phi_{0,1}\\left(\\frac{t-\\mu}{\\sigma} \\right)dt = \\frac{1}{\\sqrt{2\\pi\\sigma}}\\int_{-\\infty}^x e^{-\\frac{(t-\\mu)^2}{2\\sigma^2}}dt<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu, \\sigma,<\/span><\/span> \u0641\u0625\u0646\u0647 \u064a\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim N(\\mu, \\sigma).<\/span><\/span><\/p>\n<p><a name=\"6\"><\/a><\/br><\/br><\/p>\n<h3>\u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=2230s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644<\/span><\/strong><\/a> \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta \\gt 0<\/span><\/span> \u0644\u0647 \u062f\u0627\u0644\u0629 \u062a\u0648\u0632\u064a\u0639 \u0628\u0627\u0644\u0634\u0643\u0644<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(t) = \\left\\{\\begin{array}{llr}\n\n\\left(1 - e^{-t\/\\alpha} \\right)^\\beta &amp;;&amp; t\\geq 0 \\\\ \\\\\n\n0 &amp;;&amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644 \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha, \\beta<\/span><\/span> \u0641\u0625\u0646\u0647 \u064a\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim We(\\alpha,\\beta).<\/span><\/span> \u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644 \u0647\u0648 \u062a\u0639\u0645\u064a\u0645 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a\u060c \u0644\u0627\u062d\u0638 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">We(\\alpha,1) = Ex(\\alpha).<\/span><\/span><\/p>\n<p><a name=\"7\"><\/a><\/br><\/br><\/p>\n<h3>\u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=2311s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627<\/span><\/strong><\/a> \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta,\\alpha<\/span><\/span> \u0644\u0647 \u062f\u0627\u0644\u0629 \u0643\u062b\u0627\u0641\u0629 \u0628\u0627\u0644\u0634\u0643\u0644<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(t) = \\left\\{\\begin{array}{llr}\n\n\\displaystyle \\frac{1}{\\alpha \\Gamma(\\beta)}\\left(\\frac{t}{\\alpha} \\right)^{\\beta-1}e^{-t\/\\alpha} &amp;;&amp; t\\geq 0 \\\\ \\\\\n\n0 &amp;;&amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma(s) = \\displaystyle \\int_0^{+\\infty}u^{s-1}e^{-u}du <\/span><\/span> \u0647\u0648 \u0645\u0627 \u064a\u0639\u0631\u0641 \u0628\u0640 \u00ab\u062f\u0627\u0644\u0629 \u062c\u0627\u0645\u0627\u00bb.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u062d\u062f\u0649 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629 \u0644\u062f\u0627\u0644\u0629 \u062c\u0627\u0645\u0627 \u0647\u064a \u0623\u0646\u0647\u0627 \u062a\u0645\u0643\u0646 \u0645\u0646 \u062a\u0639\u0645\u064a\u0645 \u0627\u0644\u0639\u0648\u0627\u0645\u0644 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0625\u0644\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629 (\u0648\u062d\u062a\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0645\u0631\u0643\u0628\u0629). \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma(s+1) = s\\Gamma(s)<\/span><\/span> \u0628\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0628\u0627\u0644\u0623\u062c\u0632\u0627\u0621. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0644\u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Gamma(1)=1<\/span><\/span> \u0646\u062c\u062f \u0623\u0646<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall n\\in\\mathbb{N}\\right)\\left(\\Gamma(n) = (n-1)! \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0644\u0647 \u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627 \u0628\u0645\u0639\u0644\u0645\u0627\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta, \\alpha<\/span><\/span> \u0641\u0625\u0646\u0647 \u064a\u0643\u062a\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Ga(\\alpha,\\beta).<\/span><\/span> \u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627 \u0647\u0648 \u062a\u0639\u0645\u064a\u0645 \u0622\u062e\u0631 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a\u060c \u0644\u0627\u062d\u0638 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Ga(\\alpha,1) = Ex(\\alpha).<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0641\u064a \u0639\u0645\u0644\u064a\u0629 \u0628\u0648\u0627\u0633\u0648\u0646 \u0628\u062a\u0631\u062f\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> (\u0645\u062b\u0644 \u0627\u0644\u062a\u062d\u0644\u0644 \u0627\u0644\u0625\u0634\u0639\u0627\u0639\u064a)\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T<\/span><\/span> \u0647\u0648 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a \u0627\u0644\u0630\u064a \u064a\u0645\u062b\u0644 \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062a\u064a \u064a\u062d\u062f\u062b \u0641\u064a\u0647\u0627 \u0627\u0644\u062d\u062f\u062b m\u060c \u0625\u0630\u0646\u060c \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t\\geq 0<\/span><\/span> \u0648\u0639\u062f\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N<\/span><\/span> \u0645\u0646 \u0627\u0644\u0623\u062d\u062f\u0627\u062b \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062b \u0641\u064a \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[0,t]<\/span><\/span> \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t\\lt T \\leftrightarrow N\\lt m<\/span><\/span> \u0648\u060c \u0644\u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N\\sim Po(ct),<\/span><\/span> \u064a\u0643\u0648\u0646:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1-F_T(t) = P(T\\gt t) = \\displaystyle \\sum_{k=0}^{m-1}Po(k; ct)=e^{-ct}\\sum_{k=0}^{m-1}\\frac{(ct)^k}{k!}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0625\u0630\u0627 \u0642\u0645\u0646\u0627 \u0628\u0627\u0634\u062a\u0642\u0627\u0642 \u0647\u0630\u0627\u060c \u0633\u0646\u0643\u062a\u0634\u0641 \u0623\u0646 \u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0647\u064a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(t) = ce^{-ct}\\frac{(ct)^{m-1}}{(m-1)!}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T\\sim Ga(1\/c, m).<\/span><\/span><\/p>\n<p><a name=\"8\"><\/a><\/br><\/br><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u062b\u0627\u0628\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span> \u0628\u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\frac{c}{x^2+1}<\/span><\/span> \u0647\u0648 \u0643\u062b\u0627\u0641\u0629 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0648\u062d\u0633\u0627\u0628 \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a \u0627\u0644\u0645\u0646\u0627\u0638\u0631\u0629 (\u062a\u0648\u0632\u064a\u0639 \u0643\u0648\u0634\u064a)<\/li>\n<li>\u0645\u0646 \u062f\u0627\u0644\u0629 \u0627\u0644\u0643\u062b\u0627\u0641\u0629 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Un(a.b),<\/span><\/span> \u062a\u062d\u062f\u064a\u062f \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0646\u0627\u0638\u0631\u0629.<\/li>\n<li>\u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{\\mu,\\sigma}(x)<\/span><\/span> \u0647\u064a \u062f\u0627\u0644\u0629 \u062a\u0648\u0632\u064a\u0639 \u0627\u062d\u062a\u0645\u0627\u0644\u064a.<\/li>\n<\/ol>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/kdxgrB1h98g\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0645\u0644\u062e\u0635\u0647\u0646\u0627 \u0633\u0646\u0642\u0648\u0645 \u0628\u0641\u062d\u0635 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 \u0628\u0639\u0645\u0642\u060c \u0645\u0633\u0644\u0637\u064a\u0646 \u0627\u0644\u0636\u0648\u0621 \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u0648\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a \u0627\u0644\u062e\u0645\u0633 \u0627\u0644\u0623\u0643\u062b\u0631 \u0634\u0647\u0631\u0629: \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0623\u0633\u064a\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644 \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u060c \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (\u0627\u0644\u062c\u0648\u0633\u064a)\u060c \u062a\u0648\u0632\u064a\u0639 \u0648\u064a\u0628\u0644 \u0648\u062a\u0648\u0632\u064a\u0639 \u062c\u0627\u0645\u0627. \u0633\u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u0644 \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a\u060c \u0648\u0633\u064a\u062a\u0645 \u0641\u062d\u0635 \u0627\u0644\u0622\u062b\u0627\u0631 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0644\u0647\u0627\u060c \u0645\u062b\u0644 \u062a\u0642\u064a\u064a\u0645 \u0627\u0646\u0628\u0639\u0627\u062b \u0627\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u0641\u064a \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0645\u0634\u0639\u0629 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26864,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":177,"footnotes":""},"categories":[676,565],"tags":[],"class_list":["post-26877","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-676","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0645\u0631\u0629 - 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